Question

Four electric charges $+ q ,- q ,(+2 q )$ and $- q$ are placed at the corners of a square of side $2 L ( see$ figure). The electric potential at point $A$, midway between the two charges $+ q$ and $- q$, is :-

• A. $\frac{1}{4 \pi \in_{0}} \frac{ q }{\sqrt{5} L }$
• B. $\frac{1}{4 \pi \in_{0}} \frac{2 q }{ L }\left(1+\frac{1}{\sqrt{5}}\right)$
• C. $\frac{1}{4 \pi \epsilon_{0}} \frac{ q }{ L }\left(\frac{1}{\sqrt{5}}+\frac{1}{\sqrt{2}}\right)$
• D. Zero

Answer 1

Answer: (A)

$V_{ A }=\frac{ Kq }{ L }-\frac{ Kq }{ L }+\frac{ K (2 q )}{\sqrt{5} L }-\frac{ Kq }{\sqrt{5} L } $
$\Rightarrow V _{ A }=\frac{ Kq }{\sqrt{5} L }$